Scheduling Problems Management: Linear Programming Models


In manufacturing, scheduling issues are concerned with the processes of controlling, arranging, and optimizing both work and workloads. These processes are necessary for allocating the resources of the machinery and plant resources, the staff, raw materials, and planned production processes. Thus, inefficient scheduling can increase production times and costs, which leads to the loss of profitability. Blending technologies also play vital roles in manufacturing. They are necessary for combining several resources available to companies in order to create more products to fit the demand for them (Anderson et al., 2016).

A blending problem in manufacturing occurs when there is a lack of understanding of how to use various resources in conjunction with each other, which leads to an increase in costs and decreased profits. Logistics issues that are relevant in the manufacturing sector include the lack of efficient planning and implementation of the flow of services, goods, and related information. In many ways, logistics represents an extension of marketing because its effective integration into manufacturing maximizes the long-term profitability of firms, increases customer satisfaction, and ensures a balance between product, price, promotion, and distribution.

In the example of scheduling, linear programming models are used for identifying the optimal employment of limited resources, including human resources. In solving scheduling problems, linear programming allows formulating constraints for specific schedules and developing models for the minimum amount of resources that should be used in a manufacturing shift to reach profitability. In logistics, it is possible to use linear programming tools to optimize costs spent on transportation. For instance, mixed-integer linear programming (MILP) is an approach that can be used for finding the best possible outcome of a system with certain constraints.

The aim of the model is finding the objective function’s optimal value while also avoiding the violation of imposed restrictions. MILP can also be used when solving the problems associated with blending in manufacturing. Each source used in manufacturing has cost problems, and the blending of these sources should be done in a way that would minimize costs and satisfy the constraints of production.


The article by Hasan and Arefin (2017) is useful for improving the understanding of how linear programming can be used to improve the management of scheduling problems. The authors define issues such as insufficient methods of distributing and managing the resources during shifts. What is interesting about the study is that linear programming principles were applied to various contexts related to scheduling.

The examples included scheduling problems at police departments, restaurants, healthcare facilities, and public transport. The wide variety of examples in which linear programming is applicable and relevant shows that the quantitative method is highly useful for showing how different organizations can improve their scheduling. Using MATHEMATICA software, the researchers were successful in both formulating and solving scheduling issues and showing how resources can be distributed in order to reach the optimum level of efficiency. For instance, linear programming showed to be effective in determining the number of employees that should be scheduled for shifts.

However, despite the contribution of Hasan and Arefin (2017) into the exploration of linear programming and scheduling, the application of the quantitative method has not been explored in research literature enough. Given the positive influence of linear programming on process optimization, more research should be conducted involving multiple organizational contexts.


Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. L., Fry, M. J., & Ohlmann, J. W. (2016). Quantitative methods for business with CengageNOW (13th ed.). Boston, MA: Cengage Learning.

Hasan, M., & Arefin, R. (2017). Application of linear programming in scheduling problem. Dhaka University Journal of Science, 65(2), 145-150.


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